Photon position operators and localized bases

We extend a procedure for construction of the photon position operators with transverse eigenvectors and commuting components [Phys. Rev. A 59, 954 (1999)] to body rotations described by three Euler angles. The axial angle can be made a function of the two polar angles, and different choices of the functional dependence are analogous to different gauges of a magnetic field. Symmetries broken by a choice of gauge are re-established by transformations within the gauge group. The approach allows several previous proposals to be related. Because of the coupling of the photon momentum and spin, our position operator, like that proposed by Pryce, is a matrix that does not commute with the spin operator. Unlike the Pryce operator, however, our operator has commuting components, but the commutators of these components with the total angular momentum require an extra term to rotate the matrices for each vector component around the momentum direction. Several proofs of the nonexistence of a photon position operator with commuting components are based on overly restrictive premises that do not apply here

Photon location in spacetime

The NewtonWigner basis of orthonormal localized states is generalized to orthonormal and relativistic biorthonormal bases on an arbitrary hyperplane in spacetime. This covariant formalism is applied to the measurement of photon location using a hypothetical 3D array with pixels throughout space turned on at a fixed time and a timelike 2D photon counting array detector with good time resolution. A moving observer will see these detector arrays as rotated in spacetime but the spacelike and timelike experiments remain distinct.Comment: Equations (18) to (21) and the relevant text deleted due to an error in (20). This is no effect on the conclusions of the pape

The quantum oscillator model of electromagnetic excitations revisited

We revisit the quantum oscillator model of the electromagnetic field and conclude that, while the nonlocal positive and negative frequency ladder operators generate a photon Fock basis, the Hermitian field operators obtained by second quantization of real Maxwell fields describe photon-antiphoton pairs that couple locally to Fermionic matter and can be modeled classically. Their commutation relations define a scalar product that can be the basis of a first quantized theory of single photons. Since a one-photon state collapses to a zero-photon state when the photon is counted, the field describing it must be interpreted as a probability amplitude.Comment: 5 pages no figure